If the scalar triple product of 3 vectors a- b- and cis 0 - then they are coplanar-A- TrueB- False

The correct option is A True Look, when the volume of the parallelopipped spanned by a⃗,b⃗ and c⃗ is zero, that means it’s a flat parallelopipped with no heigh ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Scalar Triple Product

If the scalar...

Question

If the scalar triple product of 3 vectors $\to a, \to b a n d \to c$ is 0 , then they are coplanar.

True

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

False

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A
True

Look, when the volume of the parallelopipped spanned by $\to a, \to b a n d \to c$ is zero, that means it’s a flat parallelopipped with no height. It clearly means that when it’s a flat one, then all the vectors are in one plane i.e., they are coplanar.

Suggest Corrections

Similar questions

If the scalar triple product of 3 vectors $\to a, \to b a n d \to c$ is 0 , then they are coplanar.

Q. If

\to a, \to b

and

\to c

are unit coplanar vectors then the scalar triple product

[2 \to a - \to b 2 \to b - \to c 2 \to c - \to a]

is equal to

Q. If

\to a, \to b, \to c

are three unit vectors, each is inclined at an angle

\frac{π}{3}

with the other, then scalar triple product

[\to a \to b \to c]

equals

Q. The scalar triple product

[\to a + \to b - \to c \to b + \to c - \to a \to c + \to a - \to b

] is equal to

Q. Assertion :Vectors

\to a = - λ^{2}^i +^j +^k, \to b =^i - λ^{2}^j +^k

and

\to c =^i +^j - λ^{2}^k

are coplanar for only two values of

λ

. Reason: If vector

¯ x, ¯ y, ¯ z

are coplanar, then scalar triple product is zero.

Join BYJU'S Learning Program

If the scalar triple product of 3 vectors →a,→b and →cis 0 , then they are coplanar.

The correct option is A True Look, when the volume of the parallelopipped spanned by →a,→b and →c is zero, that means it’s a flat parallelopipped with no height. It clearly means that when it’s a flat one, then all the vectors are in one plane i.e., they are coplanar.

If the scalar triple product of 3 vectors $\to a, \to b a n d \to c$ is 0 , then they are coplanar.

The correct option is A
True

Look, when the volume of the parallelopipped spanned by $\to a, \to b a n d \to c$ is zero, that means it’s a flat parallelopipped with no height. It clearly means that when it’s a flat one, then all the vectors are in one plane i.e., they are coplanar.